Rought idle and poping sound

[irokdastar]

When I bought the car it was ok I had the p0011 and p0021 already on the dash . but the battery was gone I would need to jump the battery before I would start the car. till now I have no plates on the car so I didn't even drive it yet. I would just turn the car on to warm it up so it didn't sit there. At one point this weekend I tried to warm it up with a jump . it would start rev up and then shut down automatically. even if I held down the gas . I got a new battery for it yesterday and added coolant because it was low . then when I started it it would rev up and stay on but rev very hard to the point where the car would shake . If I let it idle it goes down from 200 rpm to 700 rpm and if I leave it be at one point It basically gives up and loses rev's and shuts down . but if I hold down the gas pedal all the way the revs go up slowly till around 3500 rpms and then it revs like normal . but if I let the gas go and it goes down below 3500 rpms it starts to sputter and shake and there is a loud pooping sound from under the hood. I am almost 100% sure its from the intake because the intake and filter start to jump. I will update my profile right now thank you for the heads up . I have a 2001 4.4 x5 e53. btw you been a lot of help thank you for you input. I will also upload a video of what's going on with the car once I get home tonight.